How many 3 digit numbers can be formed from the digits 1 2 3 4 5 6 7 8 9 if each digit is used only once determine how many arrangements can be found less than 300?

Answer 1

There are 9*8*7 = 504 3-digit numbers.

Of these, 112 are less than 300.

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The total ways to arrange 9 items is (9 * 8 * 7) = 504

But if the number must be less than 300, then only '1' or '2' can be

in the first position. That reduces the acceptable arrangements to 2/9 of 504 = 112. ==================================

Another way:

The first digit can be only 1 or 2 . 2 possibilities.

For each of those ...

The second digit can be any of the 9, except the one already used. 8 possibilities.

For each of those ...

The third digit can be any of the 9, except the two already used. 7 possibilities.

Total possibilities: (2 x 8 x 7) = 112